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xa. n :712:84131333 July 1, 1958 G. AGlNs ET AL 2,841,333

CALCULATING APPARATUS Filed June 15, 1942 2 Sheets-Sheet 1 mez/29 AMP.

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A oRNEYs July 1, 1958 G. AGINS ET AL 2,841,333

CALCULATING APPARATUS Y Filed June 15, 1942 2 Sheets-Sheet-Z me of s/GHT PRESE/vr P05/wmv LINE 0F FLIGHT VERTICAL PLANE l @a Y INVE N TORS 38 'EORGE AG/NS JAMES K. MACOMBER EUGENE 00/N EHARLES D. BOCA' INPUTl ATTORNEYS www@ United States Patent O CALCULATNG APPARATUS George Agins and Eugene Udin, Brooklyn, and James K.

Application June 13, 1942, Serial No. 446,886

7 Claims. (Cl. 23S-61.5)

This invention relates to computers, and more particularly to new and improved gun director calculating apparatus for predicting the angular position of a moving object or target at a predetermined instant of time after an observation of its position has been made.

More specilically, the invention has reference to gun director calculating apparatus for determining the instantaneous values of elevation lead angle V and lateral dellection angle D, which must be applied in positioning a gun in order that a projectile red from the gun when the target is at a predetermined reference position will reach a predicted target position simultaneously with the moving target.

The invention may be better understood from the following detailed description taken in connection with the accompanying drawings in which:

Figure l is a schematic diagram of gun director calculating apparatus constructed according to the invention;

Figure 2 is a velocity vector diagram of a gun lire control problem that may be solved with the gun director apparatus shown in Figure l; and

Figure 3 illustrates schematically a form of pre-amplifier that may be used in the apparatus shown in Figure l.

By way of illustration, the gun director apparatus comprising the present invention will be described in connection with the solution of a conventional Vgun fire control problem which is illustrated in Figure 2 of the drawings. Referring to Figure 2, a target T is shown as having moved along the path P1, P2, from the right of the diagram up to its present position C. In the solution of this problem, it is assumed that the target will continue along this line towards the point P2 with the same speed it has at the point C. Point A, in the diagram, represents the point of observation, as a gun director.

The problem is to determine the elevation lead angle V in a vertical plane through the line of sight and the lateral deection angle D in a slant plane perpendicular to the vertical plane through the line of sight which must be applied to the gun in order that a projectile fired when the target T is at the present position C will reach the predicted target position simultaneously with the target T.

In considering Fig. 2, it will be noted at once that this is not a diagram of relative positions of an aerial target and a gun director tracking it. The diagram, on the contrary, is a Vector diagram, that is, the length of a line does not represent a distance, but does represent a speed in linear measure, knots or yards per second, or other convenient unit. For instance, the angular arrangement of the line CE, in the ligure, gives the direction of target llight at the instant illustrated, while the length of the line is a measure of the linear speed of the target. Such a vector diagram may be arrived at very logically from the usual displacement or picture-diagram of anti-aircraft action according to the `following reasoning. If the diagram were considered to be such a simple picture-diagram, the line AC would represent the present range to the target, the line CE the distance the target travels till hit by the ICC projectile, and the line AE would be the distance the projectile travels to hit the target. The line CB would be the reduction in range which occurs during the interval of time while the projectile is so travelling. This interval of time is, of course, the time-of-llight-of-projectile, Tf, and the length CB would therefore be the rate of reduction of range, R, times this value Tf, or CB=RTf. This equation is the key to the.vector diagram of Fig. 2, because to produce it we have divided RTf by Tf in order to get vector CB=R in Fig. 2. Of course, if one value of the picture diagram is divided by Tf, so must all other values be divided or the scale would be lost. Therefore, present range R has become which is the line AC in Fig. 2, CE has become target speed and AE has become advance-range-divided by Tf, that is average-speed-of-projectile.

Of course, it may be objected, that it is hard to conceive of dividing linear quantities in a diagram by an interval of time, especially since that does not exist independently, but is itself a function of the Very values involved, and which, together with most of the linear values,

is in a state of ux. The answer is that we are dealing with a set of simultaneous equations, in which, when one term is changed, the whole set-up must be readjusted. In other words, the set-up of Fig. 2 is a regenerative vector diagram.

Range-rate R, if it is acting to increase the range, is called positive; if it is decreasing the range, it is called negative. If, in Fig. 2, it is recalled that the sight line (AC) is understood to be sweeping to the left in following the target, it will be seen that the present range is decreasing. Therefore, the range rate is negative. All the lines in Fig. 2 to the left of the target represent only fictitious or imaginary values, since they merely constitute an assumption of the future. It is further realized that the instant illustrated by Fig. 2 is that instant when the projectile is leaving the gun (understood to be at point A) along the line AE.

The vector BD is proportional to the product of the time rate of change of elevation angle and the range R,

which product will be designated (XR). Since the vectors E and 'l5 are in space quadrature and lie in the same plane, they may be added vectorially to provide a resultant vector AD and a resultant angle V. The angle V is the desired elevation lead angle of the predictor.

Further, the vector E is proportional to the product of the time rate of change of bearing angle Bs and the range R, which product will be designated (Bs R). Since the vectors ED and AD are in space quadrature and lie in the same plane, they may be added vectorially to provide a resultant vector IE and a resultant angle D. The resultant angle D is the desired bearing lead angle of the predictor.

Resultant vector EA is proportional to the predicted range R2 divided by the time of flight Tf of the shell. The quotient Rz/ T f is equal to the average velocity Va of the shell over the predicted range R2.

In accordance with the invention, the values of the elevation and bearing lead angles V and D, respectively, are solved electrically from the above mentioned vector relations by a novel regenerative gun director circuit. In this circuit, a voltage proportional to the average velocity Va of the shell over a predicted range is applied to the rotor winding of an induction regulator type resolver and the l rotor of the resolver automatically turned, if necessary, until a voltage proportional tothe product of the observed time rate of change of bearing and observed range (Bs X R) or vector DE is developed in one of the stator windings thereof.

When that condition obtains, a voltage proportional to the quantity R)2l(R/Tfj-R)2 is developed across the other stator winding of the resolver. The latter voltage is impressed on the rotor winding of a second induction regulator type resolver, and its rotor is automatically turned, if necessary, until a voltage proportional to the product of the observed time rate of change of elevation and the observed range (XR) is developed in one of the stator windings thereof. The voltage developed in the second stator winding of the second resolver for that position of the rotor is proportional to the quantity A control voltage is produced in the director which is proportional to the sum of the observed time rate of change of range R and the product of the observed range R and the reciprocal 1/ Tf of the time of tiight of the shell corresponding to the value Va impressed on the rotor winding of the iirst resolver. This control voltage, the

vector AB, is compared with the voltage developed in the second stator winding of the second resolver, and any diierence between the two voltages is employed to actuate means for adjusting the voltage proportional to the quantity l/Tf a sufficient amount to reduce the voltage difference to zero. For any adjustment of the voltage 1/ Tf, a corresponding a-djustment is made in the voltage proportional to Va, which is applied to the rotor winding of the first resolver, after it has been modiied into Va cos D by the `first resolver and then into Va cos D cos V by the second resolver, Va as applied to the first resolver being a quantity which is a function of Tf which is a function of Va, i. e., the mechanism is regenerative.

When balance is eventually attained, the angular displacements of the rotors of the iirst and second resolvers are equal, respectively, to the lateral deflection angle D and elevation lead angle V for the observed values of the quantities R, R, (XR) and (Bi-SXR) that are fed to the computer from the proper observation instrument, such as an anti-aircraft gun director, A, of which this calculating apparatus is a part and which may be of any suitable construction, such as that disclosed in application Serial No. 531,562, `tiled April 18, 1944, by Messrs. Agins, Bock and Miner, for example.

Considering now Figure 1, the gun director calculating apparatus `of the present invention comprises a conventional type potentiometer liti having a movable contact 11 engaging a non-inductive conductor 12, the terminals 13 and 13a of which are excited from a source of constant alternating voltage. The output voltage of the potentiometer which appears between the movable contact 11 and the terminal 13a is proportional to a value of the average velocity Va of the shell over the predicated range R2. This value of Va may be any operating value of the potentiometer 10 and in practice would' be the value determined by 4the angular position of the movable contact 11 of the potentiometer 1@ when the system was shut down after a previous period of operation.

The output of the potentiometer 1t) is transmitted through the conductors 14 to the input terminals 15 of a booster compensator 16, of which any hell-known electronic amplifier is an example. The function of this device is to eliminate loading of the voltage source, and to compensate for errors caused by the voltage drop due to the primary current flowing through the leakage impedance of resolver 21. The output of the booster compensator 16 is transmitted from the output terminals 17 thereof through the conductors 13 to the terminals 19 of the primary winding rotor 20 of `an induction regulator mounted in space quadrature and adapted to electrically resolve trigonometric functions from varying angles and radii. Such resolution may be carried out in a variety of ways, and is here shown as the synchro type of resolver. A resolver of this type comprises a stator of the `wellknown induction motor type having wound upon it, in 90 angle relation, the stator coils 22 and 23. An armature is provided for rotation with shaft 49 having a single winding Z0, for reception of a given quantity Va as a voltage from booster compensator 16.

The voltage impressed upon the terminals 19 of the primary `winding 2G `of `the resolver 21 causes a voltage to be developed in the stator winding 22 which is proportional to (Va sin D) or (BsXR), Which is the product of the rate of change of bearing of the target T and the range R as found by the range linder. The voltage output of the stator winding 22 is transmitted from the terminals 24 thereof and through the conductors 25 to 4the terminals 26. The terminals 26 are connected in series opposition with the terminals 27 and in series with the input terminals 28 of a voltage pre-amplifier 29. The terminals 27 have an alternating voltage impressed on them which is proportional to the value of (BsXR) as computed from observed values received from the aforementioned anti-aircraft gun director atA, for example. If the voltage impressed upon the terminals 26 differs from the voltage impressed on the `terminals 27, a ydiference voltage will be applied to the terminals 28 of the pre-amplifier 29.

As shown in greater detail in Figure 3, the input terminals 28 of the pre-ampliier 29 are connected to the primary winding 30 of a conventional type transformer 31, the secondary winding 32 of which is connected to the grids of conventional type voltage amplifying tubes 33 and 34 in the well known push-pull circuit. Inasmuch as this circuit is conventional, it will not be described in detail herein. The output circuit of the tubes 33 and 34 is connected to the primary winding 35 of an output transformer 36, the secondary Winding 37 of which is connected to the output terminals 38 of the pre-amplier 29.

The voltage output from the terminals 38 of the preamplifier 29 is transmitted to the input terminals 39 of a damping unit 40, which may be any one of the wellknown electronic damping units, such as a condenser and an inductance bridged across the output terminals 41 and resonant to the frequency of the alternating current used. This unit serves to counteract any tendency of motor 46 to oscillate about its proper angular position, by opposing any tendency of the motor armature to overshoot. The output of the damping unit 40 is transmitted from the terminals 41 thereof to the input terminals 42 of a motor ampliier 43, which may be any suitable high gain type of electronic amplifier.

The voltage output from the motor amplifier 43 is impressed upon the terminals 44 of one of the windings 45 of a conventional type two-phase induction motor 46, the rotor of which is operatively connected to the rotor 20 of the resolver 21 by a shaft 49. The other Winding 47 of the motor 46 has its terminals 48 connected to a source of constant alternating current. The windings 4S and 47 of the motor 46 are disposed in space quadrature and the voltages applied to the respective windings differ in time phase.

The characteristics of the motor 46 are such that it runs at a very low speed with a very high slip. Under these conditions, since the load on the motor 46 is never zero, its speed is a function of respective voltages irnpressed upon the windings 45 and 47. Further, since voltage of constant magnitude and frequency is impressed upon the winding 47, the speed of the motor 46 is a function of the voltage impressed upon the input terminals 44 of the winding 45.

If the Voltage at the terminals 7 is different from the voltage at the terminals 26, the winding 45 of the motor 46 will be energized and the motor 46 will drive the primary rotor winding of the resolver 21 in the proper direction to reduce the voltage difference to zero. The angular displacement of the rotor Z0 of the resolver 21 from its zero position is equal to the bearing lead angle D shown in Figure 2. This angular ydisplacement is transmitted through conventional type gearing 50 to the shaft 51 from which the output D may be obtained. y

It will be noted that vectors proportional to the voltages existing across the windings 20, 22 and 23 of the resolver 21 form a triangle that is proportional to the triangle AED of Figure 2. For example, the voltages on the windings 20, 22 and 23 are respectively proportional to the vectors EA, ED and AD of triangle AED of Figure 2.

When this series of events has occurred, the voltage developed in the second stator winding 23 of the resolver 21 is proportional to (Va cos D) or This voltage is transmitted from the stator winding 23, terminals 52 and through the conductors 53 to the input terminals 54 of a booster compensator 55, similar to the compensator 16. The output of the compensator is transmitted from the output terminals 56 thereof to the input terminals 19 of the primary rotor winding 20 of a second voltage regulator type resolver 21'. Inasmuch as the resolvers 21 and 21 and circuits in which they are connected are substantially identical, primed numerals will be used to indicate corresponding parts in the circuit of the regulator 21'.

The voltage impressed upon the primary winding 20 of the resolver 21 causes a voltage to be induced in the stator winding 22 which is proportional to the product of the time rate of change of elevation and the range R, which is designated This voltage is transmitted from the output terminals 24 of the stator winding 22 through the conductors 25 to the terminals 26. The terminals 26 are connected in series opposition with the terminals 27 and in series with the input terminals 28' of a preamplifier 29.

The terminals 27 receive from the aforementionad director at A a voltage proportional to the quantity which is computed from observed values. If this voltage is different from the voltage which appears across the terminals 26', the difference voltage is amplified by the preamplifier 29 and transmitted through the damping unit to the motor amplifier 43', the output of which is impressed upon the terminals 44' of the winding 45 of the motor 46. The other winding 47 of the motor 46' has its terminals 48 connected to the source of constant alternating current.

The voltage impressed upon the winding 45 of the motor 46 causes the latter to drive the rotor winding 20 of the resolver 21 through the shaft 49 in the proper direction to reduce the difference between the voltages existing at the terminals 26' and 27' to Zero. When that occurs, the winding 45 is deenergized and the motor comes to rest. The angle through which the rotor winding 20 of the resolver 21' is displaced from its zero position in this operation is the elevation lead angle V illustrated in Figure 2. The angular displacement of the rotor 20 is transmitted through conventional type gearing 50 to the shaft 51' from which an output of the angle V may be obtained.

Again it will be noted that vectors proportional to the voltages on the windings 20', 22 and 23 of the re- 6 solver 21' form a triangle proportional to the triangle ABD of Figure 2. For example, the voltages on the windings 20', 22' and 23 of the resolver 21' `are respectively proportional to the vectors AD, BD and AB of triangle ABD of Figure 2.

After this adjustment of the rotor winding 20 of the resolver 21 has taken place, the voltage induced in the stator winding 23 thereof is proportional to the quanthe sum of the observed rate of change R and the product of the observed range R and the reciprocal of the time of Hight l/Tf which corresponds to the value Va which was initially provided by the potentiometer 10.

The reciprocal of the time of flight l/Tf is provided by an electric cam 62 having a movable contact 65 engaging a compound conductor 63, the terminals 64 and 64a of which are connected to the constant source of A. C. supply. As shown, this electric cam 62 is essentially a potentiometer provided with intermediate taps and additional auxiliary resistors electrically connected to and between the taps to constitute the compound conductor 63, whereby predetermined voltage drops between adjacent taps are obtained, depending upon the cam design. The design curve of the cam, which is a curve of angular displacement versus voltage, is computed from the ballistic data of the gun to be used. The movable contact 65 of the cam 62 is coupled to the movable Contact 11 of the potentiometer 10 by means of the shafts 66 and 67 and the gearing 68 such that the relationship between the movable contacts 65 and 11 is always the same as the relationship between the quantities l/Tf and Va, respectively, Va being a function of Tf which in turn is a function of Va.

The output voltage of the electric cam 62 is transmitted from the movable contact 65 and the terminal 64a thereof through the conductors 69 to the input terminals 70 of a booster amplifier 71 which is similar in construction and function to the booster amplifiers 16 and 55. The output of the booster amplifier 71 is transmitted from the output terminals 72 thereof to the terminals 73 of the conductor 74 of a conventional type potentiometer 75, in which the conductor 74 is preferably a helix of constant cross-section wire wound evenly on a non-inductive ring as a support. The potentiometer 75 is provided with a movable contact 76 mounted on a shaft 77 which is displaced in accordance with values of the observed range R. This displacement of movable contact 76 results in a voltage output proportional to the product of this displacement and voltage input and hence this potentiometer gcircuit functions as a multiplier and provides an output proportional to the product of the range R and the reciprocal of the time of flight l/Tf or R/Tf.

The output of the potentiometer multiplier 75 is connected by means of the conductors 78 in series with the terminals 59 and 79. A voltage proportional to the observed rate of change R is impressed on the terminals 79. It will be apparent that this circuit impresses a voltage on the terminals 59 which is proportional to (R/Tf-l-R).

If there is any difference between the voltages appearing across the terminals 58 and 59, that difference is impressed upon the pre-amplifier 29, the output of which is transmitted through a damping unit 40 like the damping units 40 and 40', to the motor amplifier 43". The output of the motor amplifier 43 is impressed j change.

7 upon the terminals 44 of one of the windings 45 of the two-phase induction motor 46 which is similar to the motors 46 and 46. The terminals 48 of the second winding 47" of the motor 46" are connected to the source of constant alternating current.

The voltage impressed upon the winding 45 of the motor 46 causes it to drive the gearing 68 from the shaft 80, thereby adjusting the movable arm 65 of the electric cam 62 in the proper direction to reduce the difference between the voltages at the terminals 58 and 59 to zero. When that has been accomplished, the motor 46" is deenergized and comes to rest.

It will be noted that the adjustment of the movable` contact 65 of the electric cam 62 is accompanied by a corresponding adjustment of the contact 11 of the potentiometer 10. This changes the value of the voltage proportional to Va which is fed to the primary winding 26 of the resolver 21. Accordingly, the system readjusts itself further as described above to accommodate this When the system is brought into synchronism, the values of (BsXR), (EXR) and (R/Tf-l-R), which appear at the terminals 26, 26 and 58, respectively, will be equal to the corresponding values which appear at the terminals 27, 27 and 59 and which are computed elsewhere in the director from observed values. Also, the angular displacements of the rotors of the resolvers 21 and 21 from their zero positions are equal to the correct values of the lateral deflection angle D and elevation lead angle V. In this fashion, the apparatus provides a continuous solution of the lead angles V and D.

While a specific embodiment of the invention has been described in detail above, the invention is not intended to be limited thereto but is susceptible of numerous changes in form and detail within the scope of the following claims.

We claim:

l. In a computer for solving for a plurality of vector quantities that may be represented by two triangles lying in intersecting planes and having a common side, the combination of means for providing a voltage proportional to a first of said vector quantities, adjustable means having a winding energized by said voltage for inducing in adjacent windings output voltages proportional to a second vector quantity and to a third vector quantity, which third quantity represents the common side of said two triangles, means for providing a voltage corresponding to a value proportional to said second quantity, means responsive to a difference between said last-named voltage and the voltage proportional to the second vector quantity provided by said adjustable means for adjusting said adjustable means to change said voltage .difference to a predetermined value, second adjustable means having a winding energized by the voltage proportional to said third vector quantity for inducing in adjacent windings voltages proportional to a fourth and a fifth of said vector quantities, means for providing a voltage corresponding to a value proportional to said fourth vector quantity, and means responsive to any difference between said lastnamed voltage and the voltage proportional to the fourth vector quantity provided by said second adjustable means for adjusting said second adjustable means to change said voltage difference to a predetermined value, the degree of adjustment of each of said adjustable means, respectively, being a function of an angle in each of said two triangles, said last-named angles being formed by adjacent component sides of the dihedral angle forming said vector quantities.

2. In a computer for solving for aplurality of vector quantities that may be represented by two triangles lying in intersecting planes and having a common side, the combination of rst adjustable means for providing a voltage proportional to a first of said vector quantities, second adjustable means having a winding energized by said voltage for inducing in adjacent windings output voltages proportional to a second vector quantity and to a third vector quantity represented by the common side of said two triangles, means for providing a voltage corresponding to a value proportional to said second quantity, means responsive to a difference between said last-named voltage and the voltage proportional to the second vector' quantity provided by said second adjustable means for adjusting said second adjustable means to change said voltage difference to a predetermined value, third adjustable means having a winding energized by the voltage proportional to said third vector quantity for inducing in adjacent windings voltages proportional to the fourth and fifth of said vector quantities, means for providing a voltage corresponding to a value proportional to said fourth vector quantity, and means responsive to any difference between said last-named voltage and the voltage proportional to the fourth vector quantity provided by said third adjustable means for adjusting said third adjustable means to change said voltage difference to a predetermined value, means for providing a voltage proportional to a value of said fifth vector quantity which is obtained from observed values, means responsive to any'difference between said last-named voltage and the voltage proportional to the fifth vector quantity provided by said third adjustable means for adjusting said third adjustable means to change said voltage difference to a predetermined value, and means for simultaneously adjusting said first adjustable means a degree proportional to the degree of adjustment of said third adjustable means, whereby the degree of adjustment of each of said second and third adjustable means, respectively, is a function of an angle in each of said two triangles, said last-named angles being formed by adjacent component sides of the dihedral angle forming said vector quantities.

3. In a computer for solving for a plurality of vector quantities that can be represented by at least two triangles lying in intersecting planes and having a common side, the combination of an induction regulator resolver having a rotor winding and a plurality of stator windings, means for providing a voltage proportional to one of said vector quantities, means for impressing said voltage on one of said resolver windings, thereby causing voltages to be induced in the other windings thereof, means for producing a voltage corresponding to a value proportional to a second of said vector quantities, means responsive to any diiference between said last-named voltage and the voltage output of one of said resolver windings for adjusting the rotor winding relatively to the stator windings thereof to change said voltage difference to a predetermined value, whereby the voltage output of another of said resolver windings is proportional to a third of said vector quantities, a second induction regulator resolver having a rotor winding and a plurality of stator windings, an electrical circuit for impressing the voltage output of said other first resolver winding on one of the windings of said second resolver, thereby causing voltages to be induced in the other windings thereof, means for producing a voltage corresponding to a value proportional to a fourth of said vector quantities, and means responsive to any difference between said last-named voltage and the voltage output of one of said second resolver windings for adjusting the rotor winding of said second resolver relatively to the stator windings thereof to change said voltage difference to a predetermined value, whereby the voltage output of another of said second resolver windings is proportional to a fth of said vector quantities and the degrees of adjustment of the rotor windings of said first and second resolvers are functions, respectively, of an angle in each of said triangles, said last-named angles being formed by adjacent component sides of the dihedral angle forming said vector quantities.

4. In a computer for solving for a plurality of vector quantities that can be represented by at least two triangles lying in intersecting planes and having a common side, the

combination of an induction regulator resolver having a rotor winding and a plurality of stator windings, adjustable means for providing a voltage proportional to one of said vector quantities, means for impressing said voltage on one of said resolver windings, thereby causing voltages to be induced in the other windings thereof, a source of voltage corresponding to a value proportional to a second of said vector quantities, means responsive to any difference between said last-named voltage and the voltage output of one of said resolver windings for adjusting the rotor winding relatively to the stator windings thereof to change said voltage difference to a predetermined value, whereby the voltage output of another of said resolver windings is proportional to a third of said vector quantities, a second induction regulator resolver having a rotor winding and a plurality of stator windings, an electrical circuit for impressing the voltage output of said other first resolver winding on one of the windings of said secondA resolver, thereby causing voltages to be induced in the other windings thereof, a source of voltage corresponding to a value proportional to a fourth of said vector quantities, means responsive to any difference between said last-named voltage and the voltage output of one of said second resolver windings for adjusting the rotor winding of said second resolver relatively to the stator windings thereof to change said voltage difference to a predetermined value, whereby the voltage output of another of said second resolver windings is proportional to a fifth of said vector quantities, a source of voltage proportional to an observed value of said fifth vector quantity, second adjustable means responsive to any difference between said last-named voltage and the voltage output of said yother winding of said second resolver for reducing said voltage difference to a predetermined value, and means for simultaneously adjusting said first adjustable means a degree corresponding to the degree of adjustment of said second adjustable means, whereby the degrees of adjustment of the rotors of the rst and second resolvers, respectively, are functions of an angle in each of said triangles, said last-named angles being formed by adjacent component sides of the dihedral angle forming said vector quantities.

5. In a computer for solving for a plurality of vector quantities that may be represented by two right triangles lying in intersecting planes and having a common side, the combination of an induction regulator resolver having a rotor winding and two stator windings disposed in space quadrature, means for providing a voltage proportional to one of said vector quantities, means for impressing said voltage on the rotor winding of said resolver, thereby inducing voltages in the stator windings thereof, a source of voltage corresponding to a value proportional to a second of said vector quantities, means responsive to any difference between said last-named voltage and the voltage output of one of said stator windings for adjusting the rotor winding of said resolver relatively to the stator windings thereof to reduce said voltage difference to zero, whereby the Voltage induced in the second of said resolver windings is proportional to a third of said vector quantities, said three vector quantities comprising one of said right triangles, a second induction regulator resolver having a rotor winding and two stator windings disposed in space quadrature, means for impressing the voltage output of said first resolver second stator winding on the rotor winding of said second resolver, thereby inducing voltages in the stator windings thereof, a source of voltage proportional to a fourth of said vector quantities, and means responsive to any difference between said last-named voltage and the voltage output of one of said second resolver stator windings for adjusting the rotor winding of said second resolver relatively to the stator windings thereof to reduce said voltage difference to zero, whereby the voltage output of saidI second resolver second stator winding is proportional to a fifth of said vector quantities and the degrees of adjustment of the rotor windings of said first and second resolvers are equal, respectively, to an angle in each of said vector triangles, said last-named angles being formed by adjacent component sides of the dihedral angle forming said vector quantities.

6. In a computer for solving for a plurality of vector quantities that may be represented by two right triangles lying in intersecting planes and having a common side, the combination of an induction regulator resolver having a rotor winding and two stator windings disposed in space quadrature, first Kadjustable means for providing a voltage proportional to one of said vector quantities, means for impressing said voltage on the rotor winding of said resolver, thereby inducing voltages in the stator windings thereof, a source of voltage corresponding to a value proportional to a second of said vector quantities, means responsive to any difference between said last-named voltage and the voltage output of one of said stator windings for adjusting the rotor winding of said resolver relatively to the stator windings thereof to reduce said voltage difference to zero, whereby the voltage induced in the second of said resolver windings is proportional to a third of said vector quantities, said three vector quantities comprising one of said right triangles, a second induction regulator resolver having a rotor winding and two stator windings disposed in space quadrature, means for impressing the voltage output of said iirst resolver second stator winding on the rotor winding of said second resolver, thereby inducing voltages in the stator windings thereof, a source of voltage proportional to a fourth of said vector quantities, and means responsive to any difference between said last-named voltage and the voltage output of one of said second resolver stator windings for adjusting the rotor winding of said second resolver relatively to the stator windings thereof to reduce said voltage difference to zero, whereby the voltage output of said second resolver second stator winding is proportional to a fifth of said vector quantities, second adjustable means for providing ya voltage proportional to a value of said fifth vector quantity which is based on an observed value, means responsive to any difference between said last-named voltage and the voltage output of said second resolver second stator winding for adjusting said second adjustable means to reduce said voltage difference to zero, and means for simultaneously adjusting 'said first adjustable means a degree corresponding to the degree of adjustment of saidsecond adjustable means, whereby the degrees of adjustment of the rotor windings of said first -and second resolvers are functions, respectively of an angle in each of said vector triangles, said last-named angles being formed by adjacent component sides of the dihedral angle forming said vector quantities.

7. In a computer for solving for a plurality of vector quantities that may be represented by two right triangles lying in intersecting planes and having a common side, the combination of a iirst adjustable potentiometer for providing an output proportional to one of said vector quantities, an induction regulator resolver having a rotor winding and two stator windings disposed in space quadrature, electrical connections for impressing the output of said potentiometer on the rotor winding of said resolver, thereby causing voltages to be induced in the stator windings thereof, a source of voltage corresponding to a Value proportional to a second of said vector quantities, a rst electrical circuit for combining said lastnamed voltage with the voltage output of one of said resolver stator windings, motive means responsive to any voltage difference in said first electrical circuit for adjusting the rotor winding of said resolver to reduce said voltage difference to zero, whereby the voltage output of the second stator winding of said resolver is proportional to the vector quantity represented by the common side of said vector triangles, a second induction regulator resolver having a rotor winding and two stator windl 1 ings disposed in space quadrature, an electrical circuit for impressing the voltage output of said rst resolver second stator Winding on the rotor Winding of said second resolver, thereby inducing voltages in the stator windings thereof, a source of voltage corresponding to a value proportional to a fourth of said vector quantities, a second electrical circuit for combining said last-named voltage with the voltage output of one of said second resolver stator windings, motive means responsive to any voltage diierence in said second electrical circuit for adjusting the rotor winding of said second resolver to reduce said voltage diiference to zero, whereby the voltage output of the second stator winding of said second resolver is proportional to a fifth of said vector quantities, means including a second adjustable potentiometer for providing a voltage proportional to a Value of said fifth vector quantity which is derived from observed values, a third electrical circuit for combining said lastnamed voltage with the voltage output of said second resolver second stator winding, and motive means responsive to any voltage difference in said third electrical circuit for adjusting said second adjustable potentiometer to reduce said voltage diierence to zero and for simultaneously adjusting said first adjustable potentiometer in predetermined relation to the degree of adjustment of said second potentiometer, whereby the degrees of adjustment of the rotor windings of said first and second resolvers are equal, respectively to an angle in each of said vector triangles, said last-named angles being formed by adjacent component sides of the dihedral angle forming said vector quantities.

References Cited in the tile of this patent UNITED STATES PATENTS 1,154,252 Kennedy Sept. 21, 1915 1,258,032 MacGahan Mar. 5, 1918 1,641,762 `Tones Sept. 6, 1927 1,677,378 Albrecht July 17, 1928 1,814,842 Murphy July 14, 1931 1,907,804 Hausman et al May 9, 1933 2,080,186 Reymond May 11, 1937 

